Which of the function is non-differential at `x=0?` `f(x)="cos"|x|`

Which of the function is non-differential at x=0? f(x)=|"x"^3|

Which of the function is non-differential at x=0? f(x)="x"|"x"|

Which of the following function is not differentiable at x=0? f(x)={(0 ,, xgeq0),(x^2 ,, x<0):} , f(x)=x^2sgn(x)

Prove the each of the following function is differentiable at x=0. (i) f(x) = cos|x| (ii) f(x) = x|x| (iii) f(x)=|x^(3)|(iv) f(x) =(x)/(1+|x|)

Show that the function f(x)=x^(3/2) is not differentiable at x=0.

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

Drew the graph of the function and find the points of non-differentiability .(i) f(x) = min ,{x, sin x}.

Draw the graph of f(x) sin^(-1)|sin x|+cos^(-1) (cos x) . Find the range of the function. Find the points of non-differentiability. Also find the value of int_(0)^(10pi)[sin^(-1)|sin x|+cos^(-1)(cos x)] dx